Manchester City has re-established its eight-point lead over second-place Manchester United thanks to their 12th straight league win.

Wayne Rooney celebrates scoring his side's third goal of the game during the Premier League match at Goodison Park in LiverpoolPhoto:AP

Manchester City manager Pep Guardiola burst onto the field with his fists clenched and leapt into the air. Benjamin Mendy, currently out with a long-term knee injury, hobbled down the touchline in a desperate bid to get a selfie with teammate and match-winner Raheem Sterling. Ninety meters away, Southampton's players were on their backs in their own area, distraught at conceding in the sixth minute of injury time.

In a wild finale that sparked an extraordinary explosion of joy from City's players and coaching staff, Sterling curled home a last-gasp goal with virtually the last kick of the game to give the Premier League leaders a 2-1 victory over Southampton on Wednesday.

It needed something special to upstage Wayne Rooney's hat-trick goal from his own half for Everton on an incident-packed night in England's top flight.

Sterling managed it.

"It was an astonishing end to the game," said Guardiola, who was told to calm down by the referee amid his frenzied celebrations. "It means a lot."

City re-established its eight-point lead over second-place Manchester United thanks to a 12th straight league win. Late goals used to be United's forte during the glory days under Alex Ferguson, but now it is City mastering the art of scoring the last-gasp winners.

In particular Sterling, who grabbed an 84th-minute winner against Huddersfield on Sunday and also a winner in the seventh minute of injury time against Bournemouth in August.

"I could not control it," Guardiola said of his behavior after Sterling's goal, which included a bizarre confrontation with Nathan Redmond as the Southampton winger walked off the field.

"We want to win the league but you have to celebrate when you score in the last breath like that."

In the night's other highlight, Rooney demonstrated his enduring class by meeting a goalkeeper clearance with a superbly struck first-time shot from just inside his own half that arrowed into an empty net. It was his, and Everton's, third goal in a 4-0 win over West Ham.

There were also victories for Chelsea, Arsenal and Liverpool.

Here's a closer look at the action:

LAST-GASP STERLING

Raheem Sterling has now scored three late winners — two in the league and one in the Champions League — in City's last three games, a personification of the spirit Guardiola has forged in his side. The way he took his winning goal against Southampton showed the confident mood Sterling is in, the winger taking his time in a crowded area to curl home a finish into the far corner.

He has 13 goals now this season, making him City's top scorer.

Oriol Romeu looked as if he had earned a point for Southampton in the 75th minute, after Virgil van Dijk had sliced a free kick from Kevin De Bruyne into his own net to gift City the lead in the 47th minute.

ROONEY HAT-TRICK

Rooney's technique for his long-distance goal was perfect, the former England captain striking the ball firm and true as it arrowed over a raft of West Ham defenders and into the net.

"Not many in world football who could do that," injured Everton midfielder Ross Barkley tweeted.

Rooney had already scored two goals, one from the penalty spot, on what proved to be a painful return to Goodison Park for West Ham manager David Moyes, who spent 11 years in charge of Everton (2002-13). Ashley Williams scored the fourth goal as Everton moved five points clear of the relegation zone.

Sam Allardyce was in the stands and is on the verge of becoming Everton's next manager, five weeks after the firing of Ronald Koeman.

FIVE-STAR ARSENAL

Mesut Ozil inspired Arsenal to a third straight Premier League win as Huddersfield was thrashed 5-0 at Emirates Stadium. Alexander Lacazette opened the scoring after three minutes before Ozil took over the game, setting up goals for Olivier Giroud and Alexis Sanchez and then adding a fourth himself — all in the space of four minutes.

Giroud added his second to complete the rout as Arsenal climbed to fourth place.

SALAH'S DOUBLE

Mohamed Salah came off the bench to score twice in Liverpool's 3-0 win over Stoke and make it 12 goals for the season for the Premier League's leading scorer.

Sadio Mane opened the scoring for Liverpool, lofting the ball into the net as Stoke's defenders claimed it had gone out of play earlier. Liverpool jumped to fifth place.

CONTE SENT OFF

Chelsea manager Antonio Conte was sent to the stands for the second half as his team beat Swansea 1-0 for a fifth league win in six games. Conte was dismissed from the touchline by referee Neil Swarbrick moments before the interval after furiously protesting the awarding of a Swansea goal kick.

The Italian at first sat behind the dugout, but then had to move due to the proximity of his new seat to his coaching staff.